Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution
In this paper, we propose statistical inference methodologies for estimating the shape parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula...
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2024-12-01
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| author | Yan Zhuang Sudeep R. Bapat Wenjie Wang |
| author_facet | Yan Zhuang Sudeep R. Bapat Wenjie Wang |
| author_sort | Yan Zhuang |
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| description | In this paper, we propose statistical inference methodologies for estimating the shape parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> of inverse generalized Weibull (IGW) distribution. Specifically, we develop two approaches: (1) a bounded-risk point estimation strategy for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and (2) a fixed-accuracy confidence interval estimation method for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>. For (1), we introduce a purely sequential estimation strategy, which is theoretically shown to possess desirable first-order efficiency properties. For (2), we present a method that allows for the precise determination of sample size without requiring prior knowledge of the other two parameters of the IGW distribution. To validate the proposed methods, we conduct extensive simulation studies that demonstrate their effectiveness and consistency with the theoretical results. Additionally, real-world data applications are provided to further illustrate the practical applicability of the proposed procedures. |
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| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
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| spelling | doaj-art-d08f1c120bd54dcc8cb25c4e15cd7a232025-08-20T02:00:39ZengMDPI AGMathematics2227-73902024-12-011224390610.3390/math12243906Statistical Inference on the Shape Parameter of Inverse Generalized Weibull DistributionYan Zhuang0Sudeep R. Bapat1Wenjie Wang2Department of Mathematics and Statistics, Connecticut College, New London, CT 06320, USAShailesh J. Mehta School of Management, Indian Institute of Technology Bombay, Mumbai 400076, IndiaDepartment of Mathematics and Statistics, Connecticut College, New London, CT 06320, USAIn this paper, we propose statistical inference methodologies for estimating the shape parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> of inverse generalized Weibull (IGW) distribution. Specifically, we develop two approaches: (1) a bounded-risk point estimation strategy for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and (2) a fixed-accuracy confidence interval estimation method for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>. For (1), we introduce a purely sequential estimation strategy, which is theoretically shown to possess desirable first-order efficiency properties. For (2), we present a method that allows for the precise determination of sample size without requiring prior knowledge of the other two parameters of the IGW distribution. To validate the proposed methods, we conduct extensive simulation studies that demonstrate their effectiveness and consistency with the theoretical results. Additionally, real-world data applications are provided to further illustrate the practical applicability of the proposed procedures.https://www.mdpi.com/2227-7390/12/24/3906inverse generalized Weibullshape parameterestimationsequential proceduresbladder cancer |
| spellingShingle | Yan Zhuang Sudeep R. Bapat Wenjie Wang Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution Mathematics inverse generalized Weibull shape parameter estimation sequential procedures bladder cancer |
| title | Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution |
| title_full | Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution |
| title_fullStr | Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution |
| title_full_unstemmed | Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution |
| title_short | Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution |
| title_sort | statistical inference on the shape parameter of inverse generalized weibull distribution |
| topic | inverse generalized Weibull shape parameter estimation sequential procedures bladder cancer |
| url | https://www.mdpi.com/2227-7390/12/24/3906 |
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